Question: What's the first wrong statement in the proof below that $ \triangle CEF \cong \triangle CEB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. A B C D E F Givens $ \angle ABC \cong \angle CFE$ $, \ $ $ \overline{AB} \cong \overline{EF}$ $, \ $ $ \angle BAC \cong \angle CEF$ $, \ $ $ \overline{BD} \cong \overline{CF}$ $, \ $ $ \angle DBE \cong \angle CFE$ $, \ $ and $\ $ $ \angle BED \cong \angle CEF$ Proof $ \triangle CEF \cong \triangle CAB$ because ASA $ \angle ABC \cong \angle BCE$ because vertical angles are equal $ \overline{CF} \cong \overline{BC}$ because corresponding parts of congruent triangles are congruent $ \triangle DEB \cong \triangle CEF$ because AAS $ \angle ECF \cong \angle BDE$ because corresponding parts of congruent triangles are congruent $ \triangle CEF \cong \triangle CEB$ because SSS
Answer: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle BCE \cong \angle ABC$ is the first wrong statement.